CHAPTER 2 Electromagnetism and magnetic circuit

7th week

This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

Hysteresis When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed.

It must be driven back to zero by a field in the opposite direction

If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop.

The lack of re-traceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material.

Once the magnetic domains are reoriented, it takes some energy to turn them back again.

Hysteresis Loop

It is customary to plot the magnetization M of the sample as a function of

the magnetic field strength H, since H is a measure of the externally

applied field which drives the magnetization .

Variations in Hysteresis Curves

Variations in Hysteresis Curves There is considerable variation in the hysteresis of different magnetic materials

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Hysteresis Loss

• Hysteresis loop

Uniform distribution

• From Faraday's law

Where A is the cross section area

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Hysteresis Loss

• Field energy

Input power :

Input energy from t1 to t2

where Vcore is the volume of the core

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Hysteresis Loss

• One cycle energy loss

where is the closed area of B-H hysteresis loop

• Hysteresis power loss

where f is the operating frequency and T is the period

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Hysteresis Loss

• Empirical equation

Summary : Hysteresis loss is proportional to f and ABH

Eddy currents are currents induced in conductors to oppose the

change in flux that generated them.

It is caused when a conductor is exposed to a changing magnetic field

due to relative motion of the field source and conductor; or due to

variations of the field with time.

This can cause a circulating flow of electrons, or a current, within the

body of the conductor.

These circulating eddies of current create induced magnetic fields that

oppose the change of the original magnetic field due to Lenz's law,

causing repulsive or drag forces between the conductor and the

magnet.

Eddy Current Loss

To reduce amount of eddy current loss, the iron core has to be made in laminated sheets.

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Eddy Current Loss

• Eddy current Along the closed path, apply Faraday's law

where A is the closed area Changes in B → = BA changes

→induce emf along the closed path →produce circulating circuit (eddy current) in the core • Eddy current loss where R is the equivalent resistance along the closed path

me BkfP 22 W/m3

Empirical equation of eddy current loss

K = characteristic constant of the core material Bm = maximum flux density n = steinmetz exponent; vary form 1.5 to 2.5

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Core Loss

• Core Loss

losscurrenteddyP

losshysteresisPwhere

PPP

e

h

ehc

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Magnetizing Characteristics

• Behavior of flux density compared with magnetic field strength

• B-H curve or magnetizing curve

• Increased current to the coil measured the flux

B(T)

H(A/m)

Magnetization curve (B-H characteristic)

Saturation

Figure 2. : Example of BH curve NIH

AB

;

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Hysteresis

• The relationship between B and H is complicated by non-linearity and “hysteresis”